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A308412
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Indices of Gaussian primes on a square spiral.
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3
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3, 5, 7, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 60, 62, 68, 70, 76, 78, 82, 84, 88, 90, 92, 94, 98, 100, 102, 104, 108, 110, 112, 114, 118, 120, 122, 126, 128, 132, 134, 138, 140, 144, 146, 150, 152, 156, 158
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OFFSET
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1,1
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COMMENTS
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These are the numbers k > 0 such that A174344(k) + i*A274923(k) is a Gaussian prime (where i denotes the imaginary unit).
For symmetry reasons, we obtain the same sequence when considering a clockwise or a counterclockwise square spiral, or when initially moving towards any unit direction.
All terms except the first four are even.
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LINKS
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EXAMPLE
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The first terms displayed on the center of a counterclockwise square spiral are:
y\x| -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5
---+--------------------------------------------------------
+5| *--100----*---98----*----*----*---94----*---92----*
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+4| 102 *----*----*---62----*---60----*----*----* 90
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+3| * * *---36----*---34----*---32----* * *
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+2| 104 * 38 *---16----*---14----* 30 * 88
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+1| * 68 * 18 5----*----3 12 * 54 *
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0| * * 40 * * *----* * 28 * *
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-1| * 70 * 20 7----*----9---10 * 52 *
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-2| 108 * 42 *---22----*---24----*---26 * 84
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-3| * * *---44----*---46----*---48----*----* *
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4| 110 *----*----*---76----*---78----*----*----*---82
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5| *--112----*--114----*----*----*--118----*--120----*
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MAPLE
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SP:= proc(n) option remember; local k;
k:=floor(sqrt(4*n-7)) mod 4;
procname(n-1) -I*exp(I*k*Pi/2)
end proc:
SP(1):= 0:
select(i -> GaussInt:-GIprime(SP(i)), [$1..1000]); # Robert Israel, May 20 2024
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PROG
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(PARI) \\ See Links section.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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